Heyward has nine hits in his last 23 at-bats with a home run, six RBI and six runs scored.
Morrow, who remains on the 60-day disabled list, would join the Toronto bullpen since there would not be enough time to build up his arm strength for a starting role.
Galvis managed just two hits in 42 at-bats in an early-season stint with Philadelphia.
Segura has just five hits in his last 31 at-bats. He hasn't homered since slamming two on June 20.
It has been further reported that the Angels are particularly interested in Colon after having lost ace Garrett Richards for the season to injury. But Colon must pass through waivers before a trade can be worked out.
Colon has not been as effective with the Mets as he was a year ago in Oakland, but he has allowed just two runs in his last 15 innings pitched. He is 11-10 with a 3.86 ERA on the season.
Pagan has heated up recently with seven hits in the last four games.
Eaton has been sidelined with a right oblique injury sustained when he crashed into the fence trying in vain to catch a ball on Aug. 8.
He is eligible to come off the disabled list Sunday, but will spent more time with Charlotte to prepare for his return.
Hitless in six of his last nine games,
Bruce has, oddly, managed multiple hits in the other three games with two home runs and seven RBI. He boasts a still-disappointing stat line on the year of .219/.295/.380 with 14 homers in 397 at-bats.
Montero struggled to find consistency in the rotation. He managed three quality starts, but was pounded for 13 runs in 13 innings in his other three starts combined.
"We are going to look at every avenue possible," Rothschild said. "It doesn't mean we are going to do it."
Rothschild added that the Yankees could use a six-man rotation not just to protect Tanaka, but his other starters in the wake of the epidemic of arm problems in the major leagues.